Fast and Accurate Method for Doppler Averaging of Rydberg EIT Signals

TL;DR

This paper introduces a fast, exact method for Doppler averaging in Rydberg EIT signals by deriving an explicit analytic formula, significantly reducing computational time and resources compared to traditional sampling methods.

Contribution

The authors develop a novel approach that computes Doppler-averaged atomic states analytically, eliminating the need for extensive velocity sampling and solving multiple equations of motion.

Findings

Method reduces computational time by orders of magnitude.

Provides an explicit analytic formula for Doppler averaging.

Enhances efficiency in simulating Rydberg EIT signals.

Abstract

Modeling the effect of Doppler broadening due to the thermal atomic motion of Rydberg sensors typically relies on sampling a large velocity class, solving the equations of motion for each velocity, and then averaging the atomic density matrix over that velocity class. This process is inexact, slow, and presents a bottleneck in simulating Rydberg sensors. We present an approach that allows for fast, exact velocity averaging just by solving the equations of motion twice. We find the "propagator" that acts on the zero-velocity solution to generate the velocity-dependent atomic state for all velocities. By averaging this propagator over the Maxwell-Boltzmann velocity distribution of the atoms, we obtain an explicit, analytic formula that generates the averaged atomic state. This method is expected to save memory and time computational resources by one to several orders of magnitude, compared to traditional sampling approaches.